Convert the following equation into standard form.
[tex]y=-7 x+7[/tex]
[tex][?] x+y=\square[/tex]
Answer (1)
Add 7 x to both sides of the equation: y + 7 x = − 7 x + 7 + 7 x .
Simplify the equation: 7 x + y = 7 .
Identify the coefficient of x and the constant term: A = 7 and C = 7 .
Write the equation in the standard form: 7 x + y = 7 .
Explanation
Understanding the Problem We are given the equation y = − 7 x + 7 and we want to convert it into the standard form A x + y = C , where A and C are constants.
Isolating the Constant Term To convert the given equation into the standard form, we need to move the term with x to the left side of the equation. We can do this by adding 7 x to both sides of the equation:
y + 7 x = − 7 x + 7 + 7 x
7 x + y = 7
Identifying Coefficients and Constant Now, we can identify the coefficient of x as A = 7 and the constant term as C = 7 . Thus, the equation in standard form is 7 x + y = 7 .
Final Answer The equation is now in the desired standard form. The coefficient of x is 7, and the constant on the right side of the equation is 7. Therefore, the standard form of the given equation is 7 x + y = 7 .
Examples
Understanding how to convert linear equations into standard form is useful in various real-life situations. For example, if you are managing a budget where you earn $7 for every hour you work (7x) and you have a starting amount of money (y), and you want to reach a total of $7, you can represent this situation with the equation 7x + y = 7. Converting to standard form helps in easily comparing and analyzing different budget scenarios.
